Miller arrived at the Lane last week with Blades boss Danny Wilson hinting that he would make further signings before the seasons start on 18 August. He has acted quickly to draft in McMahon, 26 and Hill, 31 on free transfers.
Hill spent part of last season on loan at the Lane and played in the Play-Off Final defeat to Huddersfield Town, meanwhile McMahon has agreed a two year deal after seeing his contract ended by Middlesbrough.
The trio could feature in tomorrow nights friendly at Rotherham United, the game is sold out for Blades supporters.